We construct a model for the string group as an infinite-dimensional Lie
group. In a second step we extend this model by a contractible Lie group to a
Lie 2-group model. To this end we need to establish some facts on the homotopy
theory of Lie 2-groups. Moreover, we provide an explicit comparison of string
structures for the two models and a uniqueness result for Lie 2-group models.Comment: 32 pages; v2: uniqueness result for 2-group models added (Th. 6.5),
typo in title corrected; v3: construction of basic PU(H)-bundle discussed
(Rem. 3.9), final version to appear in IMR
